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A challenging frontier in modern statistical physics concerns systems with a small number of degrees of freedom, far from the thermodynamic limit. Beyond the general interest in the foundation of statistical mechanics, the relevance of this subject is due to the recent increase of resolution in the observation and manipulation of biological and manmade objects at micro and nanoscales. A peculiar feature of small systems is the role played by fluctuations, which cannot be neglected and are responsible for many nontrivial behaviors. The study of fluctuations of thermodynamic quantities, such as energy or entropy, goes back to Einstein, Onsager, and Kubo; more recently, interest in this matter has grown with the establishment of new fluctuation–dissipation relations, and of socalled stochastic thermodynamics. This turning point has received a strong impulse from the study of systems that are far from the thermodynamic equilibrium, due to very long relaxation times, as in disordered systems, or due to the presence of external forcing and dissipation, as in granular or active matter. Applications of the thermodynamic and statistical mechanics of small systems range from molecular biology to micromechanics, including models of nanotransport, Brownian motors, and (living or artificial) selfpropelled organisms.
Statistical Mechanics  Small Systems  Stochastic Thermodynamics  NonEquilibrium Fluctuations  Large Deviations
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This Special Issue presents research papers on various topics within many different branches of mathematics, applied mathematics, and mathematical physics. Each paper presents mathematical theories, methods, and their application based on current and recently developed symmetric polynomials. Also, each one aims to provide the full understanding of current research problems, theories, and applications on the chosen topics and includes the most recent advances made in the area of symmetric functions and polynomials.
Fubini polynomials  wtorsion Fubini polynomials  fermionic padic integrals  symmetric identities  Chebyshev polynomials  sums of finite products  hypergeometric function  Fubini polynomials  Euler numbers  symmetric identities  elementary method  computational formula  two variable qBerstein polynomial  two variable qBerstein operator  qEuler number  qEuler polynomial  Fubini polynomials  Euler numbers  congruence  elementary method  qBernoulli numbers  qBernoulli polynomials  two variable qBernstein polynomials  two variable qBernstein operators  padic integral on ?p  the degenerate gamma function  the modified degenerate gamma function  the degenerate Laplace transform  the modified degenerate Laplace transform  Fibonacci  Lucas  linear form in logarithms  continued fraction  reduction method  sums of finite products of Chebyshev polynomials of the third and fourth kinds  Hermite  generalized Laguerre  Legendre  Gegenbauer  Jacobi  thirdorder character  classical Gauss sums  rational polynomials  analytic method  recursive formula  fermionic padic qintegral on ?p  qEuler polynomials  qChanghee polynomials  symmetry group  Apostoltype Frobenius–Euler polynomials  threevariable Hermite polynomials  symmetric identities  explicit relations  operational connection  qVolkenborn integral on ?p  Bernoulli numbers and polynomials  generalized Bernoulli polynomials and numbers of arbitrary complex order  generalized Bernoulli polynomials and numbers attached to a Dirichlet character ?  Changhee polynomials  Changhee polynomials of type two  fermionic padic integral on ?p  Chebyshev polynomials of the first, second, third, and fourth kinds  sums of finite products  representation  catalan numbers  elementary and combinatorial methods  recursive sequence  convolution sums  wellposedness  stability  acoustic wave equation  perfectly matched layer  Fibonacci polynomials  Lucas polynomials  trivariate Fibonacci polynomials  trivariate Lucas polynomials  generating functions  central incomplete Bell polynomials  central complete Bell polynomials  central complete Bell numbers  Legendre polynomials  Laguerre polynomials  generalized Laguerre polynomials  Gegenbauer polynomials  hypergeometric functions 1F1 and 2F1  Euler polynomials  Bernoulli polynomials  elementary method  identity  congruence  new sequence  Catalan numbers  elementary and combinatorial methods  congruence  conjecture  fluctuation theorem  thermodynamics of information  stochastic thermodynamics  mutual information  nonequilibrium free energy  entropy production
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